It is known to fabricate monolithic filters that include Bulk Acoustic Wave (BAW) resonator devices (also known in the art as "Thin Film Bulk Acoustic Wave Resonators (FBARs)"). Presently, there are primarily two known types of Bulk Acoustic Wave devices, namely, BAW resonators and Stacked Crystal Filters (SCFs). One difference between BAW resonators and SCFs is the number of layers that are included in the structures of the respective devices. By example, BAW resonators typically include two electrodes and a single piezoelectric layer that is disposed between the two electrodes. One or more membrane layers may also be employed between the piezoelectric layer and a substrate of the respective devices. SCF devices, in contrast, typically include two piezoelectric layers and three electrodes. In the SCF devices, a first one of the two piezoelectric layers is disposed between a first, lower one of the three electrodes and a second, middle one of the three electrodes, and a second one of the piezoelectric layers is disposed between the middle electrode and a third, upper one of the three electrodes. The middle electrode is generally used as a grounding electrode.
BAW resonators yield parallel and series resonances at frequencies that differ by an amount that is a function of a piezoelectric coefficient of piezoelectric materials used to construct the devices (in addition to other factors, including the types of layers and other materials employed within the devices). By example, for a BAW resonator wherein there is a large ratio between a thickness of a membrane layer of the resonator to a thickness of a piezoelectric layer of the resonator, the frequency differential between the parallel and series resonances of the resonator is small. For BAW resonators that include electrodes and a piezoelectric layer, but which do not include membrane layers, the frequency differential between the series and parallel resonances of the devices is large. Also, the frequency differential between the series and parallel resonances of a BAW resonator is dependent on the operating frequency being employed. For example, if there is a frequency differential of 30 MHz between parallel and series resonances of a resonator that is being operated at 1 GHz, then there would be a 60 MHz frequency differential between these resonances while the resonator is being operated at 2 GHz (assuming the relative thicknesses of the resonator layers are the same in each case).
BAW resonators are often employed in bandpass filters having various topologies. By example, filters that include BAW resonators are often constructed to have ladder topologies. For the purposes of this description, ladder filters that are constructed primarily of BAW resonators are also referred to as "BAW ladder filters". The design of ladder filters is described in a publication entitled "Thin Film Bulk Acoustic Wave Filters for GPS", by K. M. Lakin et al. (Lakin), IEEE Ultrasonic Symposium, 1992, pp. 471-476. As is described in this publication, BAW ladder filters are typically constructed so that one or more BAW resonators are series-connected within the filters and one or more BAW resonators are shunt-connected within the filters. An exemplary BAW ladder filter 41 that includes two BAW resonators 42 and 43 is shown in FIG. 8d. Another exemplary (single) BAW ladder filter 44 that includes two series-connected BAW resonators 43 and 45 and two shunt-connected BAW resonators 42 and 46 is shown in FIG. 8f. An equivalent circuit of the BAW ladder filter 44 is shown in FIG. 8h. Still another exemplary BAW ladder filter 47 is shown in FIG. 8i. This filter 47 has a "balanced" topology, and is similar to the filter 44 of FIG. 8f, but also includes a BAW resonator 48 and a BAW resonator 49. An equivalent circuit of this filter 47 is shown in FIG. 8j.
BAW ladder filters are typically designed so that the series-connected resonators (also referred to as "series resonators") yield a series resonance at a frequency that is approximately equal to, or near, the desired (i.e., "design") center frequency of the respective filters. Similarly, the BAW ladder filters are designed so that the shunt-connected resonators (also referred to as "shunt resonators" or "parallel resonators") yield a parallel resonance at a frequency that is approximately equal to, or near, the desired center frequency of the respective filters.
BAW ladder filters yield passbands having bandwidths that are a function of, for example, the types of materials used to form the piezoelectric layers of the BAW resonators, and the respective thicknesses of the layer stacks of the BAW resonators. Typically, the series-connected BAW resonators of BAW ladder filters are fabricated to have thinner layer stacks than the shunt-connected resonators of the filters. As a result, the series and parallel resonances yielded by the series-connected BAW resonators occur at somewhat higher frequencies than the series and parallel resonant frequencies yielded by the shunt-connected BAW resonators (although the series resonance of each series-connected BAW resonator still occurs at a frequency that is near the desired filter center frequency on the frequency spectrum). In a BAW ladder filter, the parallel resonances yielded by the series-connected BAW resonators cause the filter to exhibit a notch above the upper edge or skirt of the filter's passband, and the series resonances yielded by the shunt-connected BAW resonators cause the filter to exhibit a notch below the lower edge of the filter's passband. These notches have "depths" that are a function of acoustic and electric losses of the series-connected and shunt-connected BAW resonators (i.e., the notch depths are a function of quality factors of the shunt and series BAW resonators).
The difference in the thicknesses of the layer stacks of the series-connected and shunt-connected BAW resonators can be achieved during the fabrication of the devices. By example, in a case in which the BAW resonators include one or more membrane layers, an additional layer of suitable material and thickness may be added to the membrane layers of the shunt-connected devices during fabrication so that, after the devices are completely fabricated, the shunt-connected devices will have thicker layer stacks than the series-connected resonators. As another example, the series resonators can be fabricated to have thinner piezoelectric layers than the shunt resonators, and/or the thicknesses of the upper electrodes of the series resonators can be reduced by a selected amount using a suitable technique, after the deposition of the upper electrode layers. These steps require the use of masking layers. Being that a parallel resonance yielded by a series-connected BAW resonator of a BAW ladder filter causes the filter to exhibit a notch above the upper edge or skirt of the filter's passband, and the series resonance yielded by a shunt-connected BAW resonator of the BAW ladder filter causes the filter to exhibit a notch below the lower edge of the filter's passband, it can be appreciated that the maximum achievable bandwidth of the filter is defined by the frequency differential between the parallel resonant frequency of the series-connected resonator and the series resonant frequency of the shunt-connected resonator. By example, consider a BAW ladder filter that includes a series-connected BAW resonator and a shunt-connected BAW resonator. The series-connected BAW resonator is assumed to have a series resonant frequency of 947 MHz and a parallel resonant frequency of 980 MHz, and the shunt-connected BAW resonator is assumed to have a parallel resonant frequency of 947 MHz and a series resonant frequency of 914 MHz. In this example, the bandwidth of the BAW ladder filter is defined by the difference between frequencies 980 MHz and 914 MHz.
The performance of BAW ladder filters may be further understood in view of the lumped element equivalent circuit of a BAW resonator shown in FIG. 4b. The equivalent circuit includes an equivalent inductance (Lm), an equivalent capacitance (Cm), and an equivalent resistance (R), that are connected in series, and a parallel parasitic capacitance (C.sub.o). The series resonance of the BAW resonator is caused by the equivalent inductance (Lm) and the equivalent capacitance (Cm). At the series resonant frequency of the BAW resonator, the impedance of the BAW resonator is low (i.e., in an ideal case, where there are no losses in the device, the BAW resonator functions like a short circuit). At frequencies that are lower than this series resonant frequency, the impedance of the BAW resonator is capacitive. At frequencies that are higher than the series resonant frequency of the BAW resonator, but which are lower than the parallel resonant frequency of the device (the parallel resonance results from equivalent capacitance (C.sub.o)), the impedance of the BAW resonator is inductive. Also, at higher frequencies than the parallel resonant frequency of the BAW resonator, the impedance of the device is again capacitive, and, at the parallel resonant frequency of the device, the impedance of the BAW resonator is high (i.e., in an ideal case the impedance is infinite and the device resembles an open circuit at the parallel resonant frequency).
For an exemplary case in which two BAW resonators (e.g., a shunt BAW resonator and a series BAW resonator) having equivalent circuits similar to the one shown in FIG. 4b are employed in a BAW ladder filter, a lowest resonant frequency of the filter is one at which the series resonance of the shunt BAW resonator occurs. At this frequency, an input of the BAW ladder filter is effectively shorted to ground, and thus a frequency response of the BAW ladder filter exhibits a deep notch below the passband of the filter. The next highest resonant frequencies of the BAW ladder filter are the series resonant frequency of the series BAW resonator and the parallel resonant frequency of the shunt BAW resonator. These resonant frequencies are within the passband frequencies of the BAW ladder filter, and are located at or near the desired center frequency of the BAW ladder filter on the frequency spectrum. At the parallel resonant frequency of the shunt BAW resonator, the shunt BAW resonator behaves like an open circuit, and at the series resonant frequency of the series BAW resonator, the series BAW resonator behaves like a short circuit (and thus provides a low-loss connection between input and output ports of the BAW ladder filter). As a result, for a case in which a signal having a frequency that is approximately equal to the center frequency of the BAW ladder filter is applied to the input of the BAW ladder filter, the signal experiences minimum insertion loss (i.e., it encounters low losses) as it traverses the filter circuit between the filter's input and output.
A highest resonant frequency of the BAW ladder filter is one at which the series-connected BAW resonator yields a parallel resonance. At this frequency, the series BAW resonator behaves like an open circuit and the shunt BAW resonator behaves like a capacitor. As a result, the filter's input and output are effectively de-coupled from one another, and the frequency response of the filter includes a deep notch above the filter's passband.
The frequency response of a BAW ladder filter that includes no tuning elements typically has deep notches and steeply-sloped upper and lower passband edges (i.e., skirts). Unfortunately, however, these types of ladder filters tend to provide poor stopband attenuation (i.e., out-of-band rejection) characteristics. An example of a measured frequency response of a BAW ladder filter (such as filter 44 of FIG. 8f) that exhibits deep notches, steeply-sloped passband edges, and poor stopband attenuation, and which includes four BAW resonators and no tuning elements, is shown in FIG. 9.
Another exemplary frequency response is shown in FIG. 8e, for the BAW ladder filter 41 of FIG. 8d. The BAW ladder filter 41 yields the frequency response of FIG. 8e assuming that 1) the resonators 43 and 42 include the layers listed in respective Tables 1 and 2 below, 2) the layers of resonators 43 and 42 have thicknesses and include the materials listed in respective Tables 1 and 2, 3) the filter 41 is connected between 50 Ohm terminals, and 4) the filter 41 includes no tuning elements.
TABLE 1 ______________________________________ SERIES BAW RESONATOR (43, 45) Layer ______________________________________ Upper electrode: 308 nm Molybdenum (Mo) Piezoelectric 2147 nm layer: Zinc-oxide (ZnO) Lower electrode: 308 nm Molybdenum (Mo) first membrane layer: 90 nm silicon-dioxide (SiO.sub.2) area of upper 225 um electrode * 225 um ______________________________________
TABLE 2 ______________________________________ SHUNT BAW RESONATOR (42, 46) Layer ______________________________________ Upper electrode: 308 nm Molybdenum (Mo) Piezoelectric 2147 nm layer: Zinc-oxide (ZnO) Lower electrode: 308 nm Molybdenum (Mo) first membrane 90 nm layer: (SiO.sub.2) second membrane 270 nm layer: (SiO.sub.2) area of upper 352 um electrode * 352 um ______________________________________
As can be appreciated in view of Tables 1 and 2, the BAW resonator 42 includes two membrane layers, and the BAW resonator 43 includes only a single membrane layer. The employment of two membrane layers in the resonator 42 causes the resonant frequencies yielded by the resonator 42 to be lower than those yielded by the series-connected resonator 43, as was described above.
The level of stopband attenuation provided by a BAW ladder filter can be increased by including additional BAW resonators in the filter and/or by constructing the filter so that the ratio of the areas of the filter's parallel-connected BAW resonators to the areas of the filter's series-connected BAW resonators is increased. FIG. 8g shows an exemplary "simulated" frequency response of the filter 44 (which includes a greater number of resonators than the filter 41), assuming that 1) the resonators 43 and 45 include the layers having the thicknesses and materials listed in Table 1, 2) the resonators 42 and 46 include the layers having the thicknesses and materials listed in Table 2, and 3) the filter 44 includes no tuning elements.
As can be appreciated in view of FIGS. 8e and 8g, the degree of attenuation provided by the filter 44 at out-of-band frequencies is improved somewhat over the attenuation level provided by the filter 41 that includes only two BAW resonators. Unfortunately, however, the employment of additional BAW resonators in a filter increases the filter's overall size and can cause an undesirable increase in the level of insertion loss of the filter. This is also true in cases in which the filter's parallel-connected BAW resonators are fabricated to have larger areas than the series-resonators. Moreover, even if such measures are taken in an attempt to improve the filter's passband response, the level of stopband attenuation provided by the filter may be insufficient for certain applications.
As shown in FIGS. 8e and 8g, the center frequencies of the passbands of respective filters 41 and 44 are located at about 947.5 MHz on the frequency spectrum, and the minimum passband bandwidth yielded by each of the filters 41 and 44 is approximately 25 MHz. As can be appreciated by those having skill in the art, these frequency response characteristics are required of filters that are employed in GSM receivers.
Another type of filter in which BAW resonators are often employed is the multi-pole filter. Multi-pole filters typically comprise either series-connected BAW resonators or parallel-connected BAW resonators, although other suitable types of resonators may also be employed such as, for example, discrete component resonators or quartz crystal resonators. Multi-pole filters that include series-connected resonators typically include passive elements, in particular, impedance inverting elements, coupled between adjacent resonators. Conversely, multi-pole filters that include parallel-connected resonators often include admittance inverting elements coupled between adjacent resonators.
An impedance inverting element transforms a terminating impedance Z.sub.b of a circuit to an impedance Z.sub.a, where: ##EQU1## and where K represents an inversion parameter for the impedance inverting element.
An admittance inverting element transforms a terminating conductance Y.sub.b of a circuit to a conductance Y.sub.a, where: ##EQU2## and where J represents an inversion parameter for the admittance inverting element.
In microwave circuits, various components may be employed as impedance inverting elements. By example, a simple impedance inverting element can be realized by employing a quarter wavelength of transmission line (at a center frequency of the transmission line). For this device, the characteristic impedance of the transmission line is the inversion parameter of the device.
In a publication entitled "Recent Advances in Monolithic Film Resonator Technology", Ultrasonic Symposium, 1986, pp. 365-369, by M. M. Driscoll et al. (Driscoll), a disclosure is made of a multi-pole filter that includes BAW resonators connected in a series configuration and a number of impedance inverting elements, in particular, inductors, that are each connected between ground and a respective node located between a respective pair of the BAW resonators.
An example of a multi-pole filter 52 is shown in FIG. 10a. The filter 52 comprises resonators X1, X2, and X3, and impedance inverting circuits 51a-51d. The resonators X1, X2, and X3 have respective impedances represented by X.sub.1 (.omega.), X.sub.2 (.omega.), and X.sub.3 (.omega.), where X.sub.j (.omega.)=.omega.L.sub.j -.sup.1 /.omega.C.sub.j, L.sub.j represents an equivalent inductance of the respective resonator, C.sub.j represents an equivalent capacitance of the respective resonator, and where L.sub.j represents an equivalent inductance of the respective resonator, C.sub.j represents an equivalent capacitance of the respective resonator, and .omega.=2.pi.f. The filter 52 also has terminating impedances represented by R.sub.a and R.sub.b.
The impedance inversion parameter of the impedance inverting circuit 51a is equal to K.sub.01, where K.sub.01 is represented by equation (1): ##EQU3## The impedance inversion parameters of the impedance inverting circuits 51b and 51c are each equal to K.sub.j,j+1, where K.sub.j,j+1 is represented by equation (2): ##EQU4## Similarly, the impedance inversion parameter of the impedance inverting circuit 51d is equal to K.sub.n,n+, where K.sub.n,n+1 is represented by equation (3): ##EQU5## In each of the above equations (1-3), the variable (Rsp) defines a reactance slope parameter of an individual resonator X1, X2, and X3. By example, a reactance slope parameter (Rsp).sub.j of a resonator may be represented by equation (4): ##EQU6## In the foregoing equations (1-4), the term .omega. represents an angular frequency variable, the term .omega..sub.0, represents a particular angular frequency, the term w represents a fractional bandwidth, the terms g.sub.n, g.sub.n+1 g.sub.0, g.sub.1, g.sub.j, and g.sub.j+1 represent normalized capacitance or inductance values of the impedance inverting circuits 51a-51d of the filter 52, R.sub.a and R.sub.b represent terminating impedances of the filter 52, and the term ##EQU7## is a reactance slope of a resonator (i.e., a derivative of the impedance of the resonator at a center frequency of the resonator (.omega..sub.o =2.pi.f.sub.o)) relative to frequency .omega.=2.pi.f.
The impedance inverting circuits 51a-51d may each include impedance inverting elements that are similar to those included in, for example, circuits 53 and 54 of FIGS. 11a and 11b, respectively. That is, each of the impedance inverting circuits 51a-51d may comprise inductors L1-L3, such as those shown in FIG. 11a, or capacitors C1-C3, such as those shown in FIG. 11b. In the circuit 53 of FIG. 11a, each of the inductors L1-L3 preferably has a same (absolute) inductance value, although the inductance values (represented by -L) of each series inductor L1 and L2 are preferably negative, whereas the inductance value of shunt inductor L3 is preferably positive (represented by +L). Also, where more than a single one of the circuits 53 is employed in a filter, the inductance values of the inductors L1-L3 of one of the circuits 53 may be different than those of the inductors L1-L3 of other ones of the circuits 53 included in the filter. Inductance values (L) for inductors L1-L3 may be calculated using the formula K =.omega.L, where K represents an impedance inversion parameter for the circuit 53.
In the circuit 54 of FIG. 11b, each of the capacitors C1-C3 preferably has a same (absolute) capacitance value, although the capacitance values (represented by -C) of each series capacitor C1 and C2 are preferably negative, whereas the capacitance value of shunt capacitor C3 is preferably positive (represented by +C). Also, where more than a single one of the circuits 54 is employed in a filter, the capacitance values of the capacitors C1-C3 of one of the circuits 54 may be different than those of the capacitors C1-C3 of other ones of the circuits 54 included in the filter. Capacitance values (C) for capacitors C1-C3 may be calculated using the formula K1=1/.omega.C, where K1 represents an impedance inversion parameter for the circuit 54.
In cases where the circuit 53 is employed within the impedance inverting circuits 51a-51d of the multi-pole filter 52 of FIG. 10a, the circuit 52 operates as if the inductors L1 and L2 (which have negative inductance values (-L)) are effectively "included" in the resonators X1-X3. For cases in which the circuit 54 is employed within each of the impedance inverting circuits 51a-51d of the filter 52, the circuit 52 operates as if the capacitors C1 and C3 (which have negative capacitive values (-C)) are effectively "included" in the resonators X1-X3. The "effective inclusion" of inductors or capacitors in resonators of a multi-pole filter will be further described below, with respect to the discussion of a multi-pole filter 52' shown in FIG. 10b.
Referring now to FIG. 10b, the multi-pole filter 52' is shown. The filter 52' is similar to the filter 52 of FIG. 10a, except that the resonators X1 and X2(for convenience, resonator X3 is not shown in FIG. 10b) are shown to include inductors and capacitors. More particularly, resonator X1 is shown to include inductor L1' and capacitor C1', and resonator X2 is shown to include inductor L2' and capacitor C2'.
In cases where the circuit 53 is employed as impedance inverting circuits 51a-51d for the multi-pole filter 52' of FIG. 10b, the filter 52' operates as if the inductors L1 and L2 of circuit 53 (which inductors have negative inductance values (-L)) are effectively "included" in resonators of the filter 52'. More particularly, and as an example, the employment of circuit 53 for impedance inverting circuits 51a and 51b connected to resonator X1 within filter 52' causes an equivalent inductance to be produced which is a combination of the inductance value of inductor L1' of resonator X1 and the inductance values of inductors L1 and L2 of the impedance inverting circuits 51b and 51a, respectively. This equivalent inductance has a value L.sub.eqv, where L.sub.eqv =L.sub.L1 -L-L, where L.sub.L1 represents the inductance value of inductor L1', and -L represents the inductance value of the individual inductors L1 and L2. This relationship can also be characterized by the equation L.sub.eqv =L.sub.L1 -.omega./K.sub.01 -.omega./K.sub.12, where .omega. represents frequency, K.sub.01 represents an impedance inversion parameter for the circuit 51a, and K.sub.12 represents an impedance inversion parameter for the circuit 51b.
In cases where the resonators of a filter are fabricated so as to exhibit similar resonant frequencies, the inclusion of impedance inverting circuits, such as circuits 51a-51d, within the filter can cause the resonators to exhibit somewhat different resonance frequencies.
A curve (CV1) representing a reactance X(.omega.) of a series resonator having one inductor and one capacitor (such as resonators X1-X3) is shown in FIG. 11c. Curve (CV2) represents the reactance of a similar resonator that is coupled to a shunt capacitor. The series resonance of the resonator for each case is represented by (SR), and the parallel resonance of the resonator coupled to the shunt capacitor is represented by (PR). As can be seen in view of FIG. 11c, the reactance curves for the series resonator and the series resonator that is coupled to a shunt capacitor resemble one other at approximately the frequencies of the series resonances of the resonators. In filters that are similar to filter 52', but which include BAW resonators for the resonators X1, X2, and X3 of FIG. 10b, this can cause the filter to yield only a narrow passband bandwidth. This is especially true if no external coil is employed in the filter for canceling the effects of the shunt capacitor near the center frequency of the filter (which causes the parallel resonant frequency of the resonator to be increased).
In cases where the circuit 54 is employed as impedance inverting circuits 51a-51d for the multi-pole filter 52' of FIG. 10b, equivalent capacitances are provided in the filter 52' which result from a combination of the capacitance values (-C) of capacitors C1 and C3 of circuit 54 and capacitance values of various ones of the capacitors C1', C2', etc., of the filter 52'. By example, the employment of circuit 54 for impedance inverting circuits 51a and 51b, which are connected to resonator X1 within filter 52', causes an equivalent capacitance to be provided which is a combination of the capacitance value of capacitor C1' of resonator X1 and the capacitance values (-C) of capacitors C1 and C3 of the impedance inverting circuits 51b and 51a, respectively. This equivalent capacitance has a value C.sub.eqv, where C.sub.eqv =C.sub.c1 -C-C, C.sub.c1 represents the capacitance value of capacitor C1', and -C represents the capacitance value of the individual capacitors C1 and C2. This relationship can also be characterized by the equation C.sub.eqv =C.sub.C1 -.omega./K.sub.01 -.omega./K.sub.12, where .omega. represents frequency, K.sub.01 represents an impedance inversion parameter for the circuit 51a, and K.sub.12 represents an impedance inversion parameter for the circuit 51b.
Filters such as that shown in FIG. 10b are preferably designed by first selecting thicknesses and areas for layers of the resonators of the filters. These thicknesses and areas are selected so that the resonators will resonate at desired frequencies. Thereafter, equivalent circuit element values (e.g., Lm, Cm and C.sub.o) are calculated, as are values (e.g., K.sub.j, K.sub.j+1) for impedance inversion parameters of the filter. Being that these impedance inversion parameter values affect the equivalent capacitance values and/or equivalent inductance values provided within the filter, the calculated values of the equivalent circuit elements (e.g., Lm, Cm and C.sub.o), as well as the thicknesses/areas of the resonator layers, may need to be modified somewhat in order to enable the resonators to resonate at desired frequencies.
An example of a multi-pole filter 55 which includes series-connected BAW resonators 56-58, and which also includes capacitors C01, C12, C23, and C34, which function as impedance inverting elements, is shown in FIG. 12. The capacitors C01, C12, C23, and C34 are shunt-connected within the circuit 55. The capacitance values of these capacitors C01, C12, C23, and C34 may be selected using known filter synthesis methods for enabling the filter 55 to produce a desired frequency response (including, e.g., a response similar to that of a Butterworth or Chebyshev filter).
Multi-pole filters such as that shown in FIG. 12 (these filters are also referred to as "BAW resonator multi-pole filters") typically provide narrow passband bandwidths. By example only, for cases in which these types of filters are operating at frequencies in the gigahertz range, the filters provide a passband bandwidth of only a few megahertz. Typically, the BAW resonators of these types of filters are designed to have a series resonance at the passband center frequency of the filters, and the passband bandwidths of the filters are more narrow than the band of frequencies which separates the parallel and series resonances of each individual BAW resonator.
The passband bandwidth of multi-pole filters that include BAW resonators can be increased by connecting other passive elements ("tuning"elements), such as inductors, in parallel with these BAW resonators, as is described in the Driscoll publication. The added inductors normally cause the equivalent parallel capacitance C.sub.0 (see, e.g., FIG. 4b) of the individual BAW resonators to be canceled at the center frequencies of the individual filters, and also increase the frequency differential between the parallel and series resonant frequencies of the respective resonators. Unfortunately, these inductors may not always be effective at out-of-band frequencies, and the addition of more than a few of these inductors to a filter can add undesired complexity and size to the overall filter structure.
An example of a filter 59 which includes inductors connected in parallel with BAW resonators is shown in FIG. 13. The filter 59 includes BAW resonators (BAW1), (BAW2), and (BAW3), inductors L.sub.01, L.sub.02, and L.sub.03, which are connected in parallel with the respective BAW resonators (BAW1), (BAW2) and (BAW3), and capacitors C01, C12, C23, and C34, which are employed as impedance inverting elements. Each of the inductors L.sub.01, L.sub.02, and L.sub.03, has an inductance value of L.sub.00, where L.sub.00 =1/(C.sub.0 .omega..sub.0.sup.2), C.sub.0 represents the equivalent parallel capacitance of individual ones of the resonators (BAW1), (BAW2), and (BAW3), and .omega..sub.o represents a center frequency of the filter 59. The filter 59 exhibits a frequency response having three poles.
The inclusion of the inductors L.sub.01, L.sub.02, and L.sub.03 in the filter 59 enables the filter 59 to provide an increased passband bandwidth relative to the filter 55 of FIG. 12. Unfortunately, however, the inclusion of the inductors L.sub.01, L.sub.02, and L.sub.03 in the filter 59 causes the filter 59 to provide poor stopband attenuation characteristics at low frequencies. This can be seen in view of FIGS. 14a and 14b, which show an exemplary frequency response of the filter 59, assuming that 1) the BAW resonators (BAW1), (BAW2), and (BAW3) include layers having the materials and thicknesses shown in Table 3, 2) the capacitors C.sub.01, C.sub.12, C.sub.23, and C.sub.34 have capacitance values similar to those shown in Table 3, and 3) the inductors L.sub.01, L.sub.02, and L.sub.03 have inductance values similar to those shown in Table 3.
TABLE 3 ______________________________________ Layer Thickness Layer Thickness Layer (BAW 1, BAW 3) (BAW 2) ______________________________________ Tuning Layer SiO2 28 nm -- Upper Electrode Au 322 nm 322 nm Piezoelectric 1430 nm 1430 nm Layer ZnO Lower Electrode Au 331 nm 331 nm Membrane Layer 242 nm 242 nm SiO2 Area of electrodes 255 um* 255 um 255 um* 255 um (Horizontal) C01, C34 4.94 pF C12, C23 8.55 pF L.sub.01, L.sub.02, L.sub.03 7.2 nH ______________________________________
Referring to FIG. 14a, it can be seen that the filter 59 exhibits poor stopband attenuation characteristics at frequencies that are below 800 MHz.
Reference will now be made to other types of multi-pole filters, namely, multi-pole filters that are primarily comprised of Stacked Crystal Filter (SCF) devices (also referred to as "SCF multi-pole filters"). It is known to employ one or more SCF devices in a passband filter. An advantage of employing SCF devices in passband filters is the better stopband attenuation characteristics provided by these filters in general, as compared to the stopband attenuation characteristics of typical BAW ladder filters (an exemplary frequency response of a SCF is shown in FIG. 8c).
An exemplary lumped element equivalent circuit of a SCF is shown in FIG. 8b. The equivalent circuit includes an equivalent inductance (2Lm), an equivalent capacitance (Cm/2), an equivalent resistance (2R), and equivalent parallel (parasitic) capacitances (C.sub.0). As can be appreciated in view of FIG. 8b, the SCF can be considered to be an LC resonator having parallel capacitances (C.sub.0) connected to ground. Owing to these parallel capacitances (C.sub.0), SCF devices are well suited for being employed in multi-pole filters. By example, an ideal multi-pole filter having SCF devices is preferably constructed so that the parallel capacitances C.sub.0 of the devices function as impedance inverting elements. The use of these capacitances C.sub.0 as impedance inverting elements avoids the need to employ external discrete components as impedance inverting elements for the filter.
In a SCF device, the maximum passband bandwidth that can be provided is a function of the ratio of the equivalent series capacitance Cm of the SCF device to the equivalent shunt capacitances C.sub.0 of the SCF device. This ratio is dependent on the level of piezoelectric coupling provided by piezoelectric layers of the SCF device. For example, a reduction in a piezoelectric layer thicknesses and a corresponding increase in a thickness of another layer (e.g., a support layer or electrode layer) of a SCF device (for causing the device to yield a same resonant frequency) results in the device yielding correspondingly narrower passband bandwidths (and decreased coupling levels). As such, the level of coupling provided may be decreased by altering the relative thicknesses of these layers. In an ideal case, a maximum passband bandwidth can be provided by a SCF device which includes only piezoelectric layers and electrode layers, although such a structure is generally not employed in practice.
In general, a maximum passband bandwidth of a filter comprised primarily of SCFs and no additional discrete elements is achieved where a combination of capacitance values (2*C.sub.0) of two series-connected SCFs of the filter equals a desired value of an impedance inverting capacitance for the filter (in such a filter, impedance inversion is provided by the combination of the capacitance values of the series-connected SCFs). An even wider passband bandwidth can be achieved by connecting an external passive element in these filters, such as an inductor, between the two SCFs devices so as to cancel at least some of the inherent shunt capacitances (C.sub.0) of the SCFs at passband frequencies. Such a filter is described in U.S. Pat. No. 5,382,930. Typically, the number of inductors employed in these types of filters is one less than the number of SCF devices employed in the filters, although additional inductors may be employed across the input ports and output ports of the filters to provide a higher degree of matching and reduced ripple levels at passband frequencies.
An exemplary multi-pole filter 56 that includes SCF devices is shown in FIG. 15a. The multi-pole filter 56 includes three SCF devices, namely SCFs 57, 58 and 59, and further includes shunt-connected inductors L.sub.p1 and L.sub.p2. FIG. 15b shows an exemplary frequency response of the filter 56 of FIG. 15a, wherein it is assumed that 1) the SCF devices 57-59 of the filter 56 include layers having the materials and thicknesses shown in Table 4, 2) each of the SCF devices 57-59 is constructed so as to yield a second harmonic resonance at the passband center frequency of the filter 56, and 3) the inductances L.sub.p1 and L.sub.p2 each have an inductance value as shown in Table 4.
TABLE 4 ______________________________________ Layer Thickness Layer (SCFs 57 and Thickness (SCF Layer 59) 58) ______________________________________ Tuning Layer SiO2 -- 107 nm Upper Electrode Au 228 nm 228 nm Upper 2020 nm 2020 nm Piezoelectric Layer ZnO Ground Electrode 317 nm 317 nm Au Lower 2020 nm 2020 nm Piezoelectric layer ZnO Lower Electrode Au 282 nm 282 nm Membrane Layer 186 nm 186 nm SiO2 Area of electrodes 310 um* 310 um 310 um* 310 um L.sub.p1 and L.sub.p2 8.3 nH inductances ______________________________________
The fundamental resonance of each SCF device 57-59 appears as a spurious response at approximately 500 MHz. Also, the parallel resonances of the shunt-connected inductors L.sub.p1 and L.sub.p2, and the equivalent parallel capacitances C.sub.0 of the SCF devices 57-59, cause the filter 56 to yield a spurious response at approximately 640 MHz. These spurious responses are undesired in that they cause the filter 56 to provide poor stopband attenuation at frequencies which are lower than the frequencies of the passband. FIG. 15c shows a portion (namely, the passband) of the frequency response of FIG. 15b in greater detail, between the frequencies of 925 MHz and 970 MHz. It should be noted that the SCF devices 57-59 of the filter 56 may also be constructed so as to yield their fundamental resonances at the passband center frequency of the filter 56. Assuming this is the case, the filter 56 may produce spurious responses at frequencies that are higher than the passband frequencies of the filter 56 (e.g., a spurious response may appear at approximately 2 GHz). This response is also undesired.
In view of the above description, it can be appreciated that it would be desirable to provide a filter having a topology which enables the filter to provide desirable passband response characteristics, such as a wide passband bandwidth and a high degree of stopband attenuation, while employing a reduced number of passive components (i.e., discrete parallel inductors and discrete impedance inverting elements) relative to the number of passive components included in prior art multi-pole filters. It would also be desirable that the filter provide better frequency response characteristics than are provided by the multi-pole filters described above.